− x^2 − 6 x + 8

Question

Samsung is also in the business of selling phones. The data for the profit that Samsung makes on selling tablets is represented by the following equation and "P(b)" and "b" being the number of blackberry phones sold (both variables in millions):

− x^ 2 − 6 x + 8

Use the quadratic formula to solve the equation. Is the vertex a maximum or minimum point? Describe what the vertex means in terms of this problem. SHOW ALL WORK!!

Answer 1

P(b) = (x) = -x^2 -6x + 8 = profits

maximum profit = 8, with x=0, as any other non-negative output level gives less profit

take the derivative and set = 0

P'(b) =-2x -6 = 0

x =6/2= -3

max profit = -(-3)^2 -6(-3) + 8 = -9+18+8= 17 with negative output of -3

but that seems to have no real counterpart in business other than possibly buying up 3 million to cut back on production available to the public, such as when OPEC cut back on oil to drive up prices. Similar to the recent oil shortage caused by a Russian hacker that sent gas prices over $3 per gallon and up to $9 in some places.

-x^2 -6x + 8

= -(x^2 +6x - 8)

= -(x^2 +6x + 9) +8+9

=-(x+3)^2+ 17 which has vertex (-3,17) which is a profit maximizing point with output = x = -3 and profit=17

with a negative coefficient of the x^2 term, the vertex is a maximum point of a downward opening parabola.

Possibly you hit the - sign when you meant =? the keyboard keys are close together. if so, then

P(x) =x^2 -6x + 8 and

P'(x) =2x-6x =0

x =6/2 = 3 = profit minimizing output level with P=9-18+8 = 1. Maximum profit would be an infinite output level.

x^2 -6x + 8

= (x^2-6x + 9) +8 -9

=(x-3)^2 -1

vertex is (3,1) a minimum profit level of $1 million at output of 3 million